Newest papers

Common Signals, Spurious Cross-Excitation, and Identification in Multivariate Hawkes Processes

Jiwon Jung, Kiseop Lee · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.19428 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

Los modelos de Hawkes multivariados se utilizan ampliamente para medir las interacciones endógenas en los datos de eventos, pero los señales comunes latentes pueden generar excitación aparente incluso sin interacción estructural. Caracterizamos la proyección lineal resultante y construimos procesos de Hawkes estables, no negativos que comparten la intensidad media y el espectro de Bartlett de los modelos de señales comunes a pesar de tener diferentes mecanismos de excitación. Esto establece una forma concreta de no identificación de segundo orden. Derivamos acumuladores de tercer orden integrados para los procesos de Hawkes con inmigración de Cox y establecen la identificación local genérica de parámetros estructurales normalizados en sistemas de dos y tres dimensiones. Un experimento de equivalencia exacta de Monte Carlo demuestra cómo la información de tercer orden

Machine translation (Meta M2M100); the English original follows.

Abstract

Multivariate Hawkes models are widely used to measure endogenous interactions in event data, but latent common signals can generate apparent excitation even without structural interaction. We characterize the resulting linear projection and construct stable, nonnegative Hawkes processes that share the mean intensity and Bartlett spectrum of common-signal models despite having different excitation mechanisms. This establishes a concrete form of second-order non-identification. We derive integrated third-order cumulants for Hawkes processes with Cox immigration and establish generic local identification of normalized structural parameters in two- and three-dimensional systems. An exact-equivalence Monte Carlo experiment demonstrates how third-order information can distinguish mechanisms with identical second-order structure, while revealing substantial finite-sample limitations under weak signals. For a restricted parametric family, we develop Whittle estimation from binned counts, establish consistency and asymptotic normality under appropriate identification conditions, and construct feasible sandwich standard errors accounting for estimated mean intensities. Simulations assess structural recovery and inference accuracy. An application to cryptocurrency transactions illustrates the sensitivity of inferred excitation to model specification and the limitations of structural interpretation based on spectral fit alone.

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Topics: Spurious relationship, Consistency (knowledge bases), Identification (biology), Parametric statistics, Event (particle physics), Mathematics

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